To perform such a localisation, a large amount of echoes is usually collected and processed to determine various distances of the reflecting scatterers along associated directions of arrival of reflected waves. This processing requires robust and efficient methods. In particular, it is very often needed for the computational load to remain limited enough to enable the in-line production of soundings from the recorded signals.
These requirements are blatant in the field of bathymetry where the cost of surveys can be very high and there is a compelling need for reliable and cost effective solutions.
High resolution imaging techniques are known but are marginally qualified for these tasks because of their large computational cost and the fact that distributions of the scatterers usually do not fit the problem of resolving a finite number of closely spaced reflectors.
Others methods, based on interferometry, are for instance described in “Multibeam sonar bottom detection using multiple subarrays” by L. Yang and T. Taxt published in Proc. OCEANS '97, vol. 2, pages 932-938, 1997. These methods will be referred to as “Sub-Array Interferometric Techniques” (SAIT) in the following description.
In the SAIT methods, measurements are performed by transmitting a wave with an across-track fan geometry covering typically more than a 90°-wide sector. The reflected wave is acquired with a receiving antenna having a large array of transducers. An example of suitable acquisition system is for instance a “Multi-Beam Echo-Sounders” (MBES). To process the acquired signals, the array of transducers is divided into two sub-arrays. A pair of beams focused in the same direction can then be formed by combining the properly synchronized respective signals of these respective sub-arrays (sometimes called beamforming), thus giving two sets of focused samples {xk} and {yk} where k are the respective indexes of transducers elements in the associated sub-arrays.
An interferometric estimator Y can for instance be computed as:
  Y  =                    s        a            ⁢              s        b        *            ⁢                          ⁢      with      ⁢                          ⁢              s        a              =                            1                      n            -            p                          ⁢                              ∑                          u              =              1                                      n              -              p                                ⁢                                          ⁢                                    x              u                        ⁢                                                  ⁢            and            ⁢                                                  ⁢                          s              b                                          =                        1                      n            -            p                          ⁢                              ∑                          v              =                              p                +                1                                      n                    ⁢                                          ⁢                      x            v                              
The complex interferometric estimator Y(t,ψ) can be mapped as a sectorial image made of a collection of beams where the range is associated with time and the angle is associated with the directions of the beams.
The problem is then to determine the direction of a specific scatterer with respect to the direction of the beam. Echoes from scatterers located in a resolution cell results in a complex interferometric estimator Y whose complex phase ηY=arg Y can be related to the angular difference between the beam axis ψ and the actual direction ψ+θ of the scatterers. With suitable parameters, in particular with a sufficient incidence of the beam on the reflecting scatterer or scatterers (for the angular footprint of the signal to be smaller than the angular resolution of the beam), the interferometric estimator Y is made of echoes whose origin sweeps the reflecting scatterer around the beam axis. Hence the complex phase of the interferometric estimator Y in function of the time of acquisition can present a ramp that is likely to cross the zero phase axis at a time corresponding to the direction of the beam axis, i.e. when θ=0. The soundings are thus determined at fixed directions ψ by deriving the range from a linear regression of said phase ramp ηψ(t) in a proper time window.
However, the SAIT methods show several drawbacks. First, it is not possible to easily determine which parts of the acquired time signals are to be processed to determine the detection of echoes from actual targets. Moreover, the relation between the complex phase of the interferometric estimator Y and the direction of arrival of the received echo η(θ) is multivalued, the complex phase having an ambiguity modulo 2π. Also, the interferometric estimator Y is not normalized and the phase ramps have thus to be detected by using miscellaneous tricks, mostly based on the magnitude of echoes, continuity of the tracked profile within the ping and inter-pings. These tricks are frequently not fully reliable and/or are based on too restrictive assumption (e.g. no more than one single interface in each direction).
There is thus a need for a cost effective and reliable method and system for determining a location of a reflecting scatterer in a medium. Such a method and system could, among other advantages, promote safety of navigation by improving bathymetry processing.